Apparently, Moveon.org has filed a complaint with the Federal Trade Commission claiming that Fox News Channel’s slogan "fair and balanced" violates the FTC’s prohibition against deceptive advertising. (Source, although there are probably others).
I’m not sure what Moveon.org hopes to achieve — they are unlikely to win, in my view. However, they will clearly cause a lot of damage and embarrassment to Fox along the way. That’s probably why they are doing it.